scholarly journals Associated orthogonal polynomials of the first kind and Darboux transformations

2021 ◽  
pp. 125883
Author(s):  
J.C. García-Ardila ◽  
F. Marcellán ◽  
P.H. Villamil-Hernández
Keyword(s):  
Orthogonal Polynomials ◽  
Darboux Transformations

scholarly journals On the Darboux transformations and sequences of p-orthogonal polynomials

2020 ◽  
Vol 382 ◽  
pp. 125337 ◽  
Author(s):  
D. Barrios Rolanía ◽  
J.C. García-Ardila ◽  
D. Manrique
Keyword(s):  
Orthogonal Polynomials ◽  
Darboux Transformations

scholarly journals Exceptional Legendre Polynomials and Confluent Darboux Transformations

2021 ◽  
Author(s):  
María Ángeles García-Ferrero ◽  
◽  
David Gómez-Ullate ◽  
Robert Milson ◽  
◽  
...  
Keyword(s):  
Orthogonal Polynomials ◽  
Legendre Polynomials ◽  
Eigenvalue Problems ◽  
Jacobi Polynomials ◽  
The Novel ◽  
Darboux Transformations ◽  
Polynomial Sequences ◽  
New Construction ◽  
Sturm Liouville ◽  
Exceptional Orthogonal Polynomials

Exceptional orthogonal polynomials are families of orthogonal polynomials that arise as solutions of Sturm-Liouville eigenvalue problems. They generalize the classical families of Hermite, Laguerre, and Jacobi polynomials by allowing for polynomial sequences that miss a finite number of ''exceptional'' degrees. In this paper we introduce a new construction of multi-parameter exceptional Legendre polynomials by considering the isospectral deformation of the classical Legendre operator. Using confluent Darboux transformations and a technique from inverse scattering theory, we obtain a fully explicit description of the operators and polynomials in question. The main novelty of the paper is the novel construction that allows for exceptional polynomial families with an arbitrary number of real parameters.

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